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feynMF:
Drawing Feynman Diagrams
with LATEX and METAFONT
Thorsten Ohly
Technische Hochschule DarmstadtSchlogartenstr. 9D-64289
Darmstadt
Germany
December 2, 1996
Abstract
feynMF is a LATEX package for easy drawing of professional
qualityFeynman diagrams with METAFONT (or METAPOST). feynMF lays
outmost diagrams satisfactorily from the structure of the graph
without anyneed for manual intervention. Nevertheless all the power
of METAFONT(or METAPOST) is available for obscure cases.
Copying
feynMF is free software; you can redistribute it and/or modify
it under theterms of the GNU General Public License as published by
the Free SoftwareFoundation; either version 2, or (at your option)
any later version.feynMF is distributed in the hope that it will be
useful, but without any war-ranty ; without even the implied
warranty of merchantability or tness for aparticular purpose. See
the GNU General Public License for more details.You should have
received a copy of the GNU General Public License along withthis
program; if not, write to the Free Software Foundation, Inc., 675
Mass Ave,Cambridge, MA 02139, USA.
This is feynmf.dtx, version v1.08, revision 1.30, date
1996/12/02.ye-mail: [email protected]
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Contents
1 Introduction 41.1 Purpose and scope . . . . . . . . . . . . .
. . . . . . . . . . . . . 41.2 Relation to similar packages . . . .
. . . . . . . . . . . . . . . . . 51.3 Historical note . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 61.4 Architecture . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 61.5
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 6
2 Usage 82.1 LATEX package and environments . . . . . . . . . .
. . . . . . . . 82.2 Auxiliary les . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 92.3 Running METAFONT . . . . . . . . . .
. . . . . . . . . . . . . . . 102.4 The feynmf perl script . . . .
. . . . . . . . . . . . . . . . . . . . 122.5 Vertex mode . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.1 External vertices . . . . . . . . . . . . . . . . . . . .
. . . 142.5.2 Arcs and internal vertices . . . . . . . . . . . . .
. . . . . 142.5.3 Polygons . . . . . . . . . . . . . . . . . . . .
. . . . . . . 182.5.4 Color . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 192.5.5 Examples . . . . . . . . . . . . . . . .
. . . . . . . . . . . 192.5.6 Labels . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 232.5.7 Manipulating the layout . . . .
. . . . . . . . . . . . . . . 242.5.8 Skeletons . . . . . . . . . .
. . . . . . . . . . . . . . . . . 252.5.9 Pulling strings . . . . .
. . . . . . . . . . . . . . . . . . . 27
2.6 Miscellaneous commands . . . . . . . . . . . . . . . . . . .
. . . . 292.6.1 Graphs in graphs . . . . . . . . . . . . . . . . .
. . . . . . 292.6.2 Reusing diagrams . . . . . . . . . . . . . . .
. . . . . . . . 302.6.3 Grouping . . . . . . . . . . . . . . . . .
. . . . . . . . . . 302.6.4 Changing parameters . . . . . . . . . .
. . . . . . . . . . 312.6.5 Shrinking . . . . . . . . . . . . . . .
. . . . . . . . . . . . 312.6.6 Debugging . . . . . . . . . . . . .
. . . . . . . . . . . . . . 312.6.7 Multiple vertices and arcs . .
. . . . . . . . . . . . . . . . 31
2.7 Immediate mode . . . . . . . . . . . . . . . . . . . . . . .
. . . . 322.7.1 Arcs . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 332.7.2 Vertices . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 332.7.3 Declarations . . . . . . . . . . . . .
. . . . . . . . . . . . . 332.7.4 Assignments . . . . . . . . . . .
. . . . . . . . . . . . . . 342.7.5 Examples . . . . . . . . . . .
. . . . . . . . . . . . . . . . 34
2.8 Raw METAFONT . . . . . . . . . . . . . . . . . . . . . . . .
. . . 352.8.1 Extending feynMF . . . . . . . . . . . . . . . . . .
. . . . 36
2.9 Common traps, trouble shooting and frequently asked
questions(FAQs) . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 392.9.1 ! Value is too large . . . . . . . . . . . . .
. . . . . 392.9.2 Diagrams in the document are never updated . . .
. . . . 402.9.3 Disgrams show up in the wrong spot . . . . . . . .
. . . . 402.9.4 Spurious labels show up . . . . . . . . . . . . . .
. . . . . 40
2.10 Known bugs . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 412.10.1 Chaotic manual . . . . . . . . . . . . . . . .
. . . . . . . . 412.10.2 Delayed error messages . . . . . . . . . .
. . . . . . . . . 412.10.3 Multiple tadpoles . . . . . . . . . . .
. . . . . . . . . . . . 41
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2.10.4 Hard limits . . . . . . . . . . . . . . . . . . . . . . .
. . . 41
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1 Introduction
1.1 Purpose and scope
In recent years, TEX1 [1] and LATEX
2 [2] have revolutionized the way we shareinformation in
theoretical physics (and other areas). Not only does TEX
providetypographical capabilities, which transcend those of
commercial \wordproces-sors" substantially, TEX documents are also
completely portable. Since imple-mentations are available on
essentially all computers in use in the community,documents can be
shared without the usual restrictions of proprietary data for-mats.
This has enabled us to collaborate on papers with colleagues on the
otherside of the globe, to replace the mailing of hard copy
preprints by electronictransmission and to submit these papers
electronically to the publisher.This portability comes with a
price, though. TEX (and LATEX) do not addressthe issue of graphical
information, apart from the rudimentary (but very
useful)capabilities of the LATEX picture environment and similar
packages [3]. As ande facto standard for the inclusion of more
complex graphics has emerged theinclusion of PostScript3 les. The
complete document can then be printed onany PostScript device.Still
there are areas, where complementary approaches seem worth
pursuing.In particular this is the case, if the graphical
information is highly formalized,like the case at hand. Feynman
diagrams are specied by their topology andthe type of particles
connecting the vertices. Thus a given diagram can bereproduced from
a very concise specication, if the software is able to choose
areasonable layout (semi-)automatically.METAFONT
4 [4] and METAPOST5 [5] appear to be the perfect tool for such
apurpose, since
1. METAFONT is part of any (reasonable) TEX installation, thus
available toall potential users,
2. both have very powerful graphics primitivs, which allow high
quality out-put, and
3. both have builtin linear algebra, which allows us to choose a
layout auto-matically.
Still, providing at least the basic interface in LATEX macros
seems appropriatefor boosting the acceptance among the less
technically oriented parts of theaudience. Thus feynMF6 [6, 7] was
conceived.feynMF is unique among packages for drawing Feynman
diagrams in combiningthe following features:
Simplicity and conciseness for common diagrams. E.g. the
scattering dia-gram in gure 1 can be specied completely in ve lines
of LATEX:
1TEX is a trademark of the American Mathematical Society.2LATEX
might be a trademark of Addison Wesley Publishing
Company.3PostScript is a trademark of Adobe Systems Inc.4METAFONT
is a trademark of Addison Wesley Publishing Company.
5John Hobby's METAPOST is a modied version of METAFONT which
generates (encap-sulated) PostScript output. METAPOST can be build
trivially on top of the web2c version ofTEX and METAFONT for UNIX.
Ports to other systems should be simple.
6feynMF is not anybody's trademark.
4
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q
Figure 1: Simple scattering diagram.
\begin{fmfgraph*}(40,30) \fmfpen{thick}
\fmfleft{i1,i2} \fmfright{o1,o2}
\fmf{fermion}{i1,v1,o1} \fmf{fermion}{i2,v2,o2}
\fmf{photon,label=$q$}{v1,v2} \fmfdot{v1,v2}
\end{fmfgraph*}
Expressiveness for complicated diagrams (see the examples
below). Extensibility (e.g. see section 2.8.1). Arbitrary
TEX-labels. This point is more important than it may seemat rst
glance because most graphical layout systems lack the power
toproduce complicated mathematical expressions. Having matching
fonts intext, equations and diagrams is also an important
esthetical feature.
1.2 Relation to similar packages
Before we start, a couple of words about some complementary
packages on themarket are in order:
Michael Levine's feynman package [8] is implemented on top of
the stan-dard LATEX picture environment [2]. This makes it
completely portable(no need for a correct METAFONT installation),
but it requires manuallayout and the graphics output is (though
very useful) less than perfect.
Jos Vermaseren's axodraw package [9] uses \specials to access
PostScriptprimitives for drawing diagrams. This approach is
inherently not portable(the ubiquity of PostScript printers makes
this a minor point, though) butas exible as the present one.
Nevertheless, it still requires manual layoutfor all diagrams.
Last, but not least, I have to mention Thomas Leathrum's mfpic
[10],which provided the inspiration for moving feynMF's user
interface fromMETAFONT to TEX. It might not have been unreasonable
to design andimplement feynMF as a package on top of mfpic, but
closer inspectionshows that feynMF and mfpic are fairly orthogonal.
mfpic is most usefulfor handling simple graphical building blocks
in formally unconstrainedcontexts. feynMF on the other hand excels
in the formal context of Feyn-man diagrams (or any other labeled
graphs for that matter), which canbe drawn automatically from a
specication.
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1.3 Historical note
Parts of this code have a rather long history7. Some of the
drawing primitivesstarted in 1989 as feynman.mf, a library of
METAFONT macros for drawingFeynman diagrams in my thesis. The
layout had to be specied completely byhand, which required a long
edit-process-preview cycle and made feynman.mfawkward to use.
Nevertheless, it suited my and other's neeeds and survivedfor ve
years without major modications. Early in 1994, I became aware
ofThomas Leathrum's mfpic [10]. This inspired me to shift the user
interfacefrom METAFONT to LATEX, because this allows a smoother
blending of theLATEX picture environment with feynMF for the
purpose of labeling the graphs.While doing this and after having
been taught by Tim Stelzer's and Bill Long'sMADGRAPH [11] that
simply minimizing the length of the graph gives much betterresults
than I had anticipated, I added the graph manipulation and layout
code.
1.4 Architecture
Even though there has never been a proper design phase in the
development offeynMF, a certain structure has emerged, which is
depicted in gure 2. A userwho is aware of this architecture should
be able to use feynMF more eectively.The most crucial aspect of the
architecture is the existence of two distinct modeswith dierent
fundamental datatypes:
vertex mode, which deals with graphs as structures consisting of
verticesand arcs and (almost) never deals with their physical
locations.
immediate mode, which deals with METAFONT paths and pairs (i.e.
co-ordinates) and allows complete control over the physical
locations.
It is of course possible to mix these modes in advanced
applications. Commandsare provided to translate vertices and arcs
to pairs and paths and vice versa.Novice users with little
experience in METAFONT programming should startwith vertex mode to
get their job done. Later, immediate mode can be used tocreate more
and more complex diagrams. It is possible to create most
diagramsthat can actually be calculated in vertex mode. Immediate
mode is most usefulfor extending line feynMF and for drawing
diagrams with fancy decorations.A word on portability: feynMF is
implemented as a LATEX package. But itshould be straightforward to
adapt it to other TEX macro packages becauseLATEX macros have been
used for convenience only and can easily be replaced orprovided in
a compatibility package. The LATEX specic environment constructcan
also easily be replaced by the equivalent construct in another
macro package.
1.5 Conclusion
It goes without saying that feynMF is not perfect. There might
be cases whereusing a graphical drawing tool with a mouse can give
more pleasing results inless time. But in most cases, feynMF will
give satisfactory results without anyne tuning. These will be
reproducible and independent from the computer itis running on.
7Which is a partial explanation, if not excuse, for its slightly
incoherent structure.
6
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\fmfforce
vloc
vpath
\fmfcmd
Immediate Mode
Objects:pairspaths
Commands:\fmfi{}{}
\fmfiv{}
\fmfiequ{}
...
Vertex Mode
Objects:vertices
arcspolygons
Commands:\fmf{}{}
\fmfv{}{}
\fmfleft{}
...
LaTEX
METAFONT
Figure 2: Architecture of feynMF: the two modes of feynMF
(immediate modeand vertex mode) both interact with LATEX and
METAFONT (or METAPOST,respectively), but operate on dierent data
types.
Early user reponses have been very encouraging. There seems to
be a rela-tively steep learning curve for those LATEX users that
have to nd out how torun METAFONT on their systems. But once this
purely technical obstacle hasbeen surmounted, users have been
enthusiatic as well about the quality of thegenerated graphs as
about the ease of use of feynMF.
7
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2 Usage
In addition to this manual, there exists also a concise
description of feynMF ina journal article [6], as well as a three
part tutorial [7].
2.1 LATEX package and environments
Instructing LATEX to use feynMF is as simple as8
\usepackage{feynmf}
If you have METAPOST, then you can use it alternatively by
placing
\usepackage{feynmp}
in your LATEX source.9
feynMF has to switch interactions mode and switches to
\errorstopmode, be-cause it is impossible in TEX to switch back. If
a dierent default is required (forautomated preprint processing, in
particular), it can be specied as a packageoption:
\usepackage[errorstop]{feynmf}
\usepackage[scroll]{feynmf}
\usepackage[batch]{feynmf}
\usepackage[nonstop]{feynmf}
All descriptions that should go into one METAFONT le are placed
inside afmffilefmffile environment which takes the name of the
METAFONT le as an argu-ment:
\begin{fmffile}{hMETAFONT-lei}. . .
\end{fmffile}
8As given, this applies to LATEX. But the installation le
feynmf209.ins allows to generatespecial versions feynmf209.sty and
feynmp209.sty which are compatible with the obsoleteLATEX version
2.09. These les are to be used as documentstyle options
\documentstyle[...,feynmf209,...]f...gor
\documentstyle[...,feynmp209,...]f...gIf you cannot use epsf.sty
for including PostScript les, you can either hack feynmp209.styor
upgrade to LATEX2e. Please keep in mind that feynMF has been
developed for LATEX2"and the LATEX 2.09 compatibility version will
always be a retrotted hack. I will accept bugreports for the 2.09
version, but I urge everybody to move to LATEX2e, which is the one
andonly supported LATEX right now.
9feynMF understands an option pre-1.03, that is of interest for
veteran users:
\usepackage[pre-1.03]ffeynmfgor
\usepackage[pre-1.03]ffeynmpgThe purpose of this option is to
enable processing of old input les (pre v1.02) that use\noexpand in
labels. Since the method for processing these les can clash (in
rare cases) withLATEX2"'s font loading procedure, it has been
disabled by default.
8
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Upto 255 graphs can be placed into one METAFONT le. Currently
feynMFdoes not check that the 255 graph limit per le is not
overrun.10 Note thatthe lename for the METAFONT le given in the
argument of the fmffileenvironment must not be identical to the
LATEX source le name, because theMETAFONT .log would be overwritten
and LATEX can no longer access theinformation in this .log le. It
should be obvious that any umber of diagramscan be generated by
using more than one fmffile environment with dierentlenames.The
fmfgraph environment contains the description of a single Feynman
dia-fmfgraphgram which will be placed a the location of the
environment. Arguments arethe width and the height of the diagram,
in units of \unitlength:
\begin{fmfgraph}(hwidthi,hheighti). . .
\end{fmfgraph}
This environment does not support labels, use fmfgraph* if your
diagramscontains labels.Same as fmfgraph, but enclosed in a picture
environment of the same size andfmfgraph*supporting LATEX
labels.
\begin{fmfgraph*}(hwidthi,hheighti). . .
\end{fmfgraph*}
Allows to allocate additional space around a fmfgraph*, since
the labels (or the\fmfframediagram itself) might overshoot:
\fmfframe(hlefti,htopi)(hrighti,hbottomi){hbox i}puts an
invisible frame of the given dimensions (measured in
\unitlength)around hbox i.
2.2 Auxiliary les
feynMF needs to share information between METAFONT and LATEX.
For thistask several auxiliary les are needed. The ow of
information depicted ingures 3 and 4 looks much more complicated
than it is. The important featureis that there a two sets of les
which can be used to distribute a document:
1. I the recipient has a working METAFONT installation (which
shouldn't bea problem, except for some impoverished commercial
implementations),the document can be typset from the LATEX source
alone, by runningLATEX, METAFONT and LATEX again (the latter step
might have to berepeated to get cross references right).
2. Another possibility (which doesn't require METAFONT on the
recipient'sside), is to distribute the LATEX source, the tfm and gf
les (or pk lesrespectively) along with the label les with extension
tn (where n as an
10There is also a very primitive, but (unfortunately) popular
operating system, which re-stricts lenames to eight characters with
a three character extension. On this system, only 99graphs can be
placed into one METAFONT le because auxiliary les will not be
unambiguous,if more than two digits are used.
9
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% foo.tex
...
\usepackage{feynmf}
...
\begin{fmffile}{fd}
\begin{fmfchar*}(100,50)
...
\end{fmfchar*}
...
\end{fmffile}
...
% fd.mf -- do not edit
input feynmf
beginchar(1,100*1pt#,50*1pt#,0);
vinit;
...
vfreeze;
vdraw;
endchar;
...
LaTEX labelsfd.log
font metricinformationfd.tfm
font bitmapfd.300gf
LaTEX labelsfd.t1
LaTEX labelsfd.t2
device independentoutput lefoo.dvi
printerlpr
latex foo
latex foo
mf fd
dvixx foo
Figure 3: Interdependency of les in a feynMF application. The
arrows showwhich les are updated in the two LATEX passes, the
METAFONT pass and thenal dvi translation step.
integer). Distributing the METAFONT log les is a possible
alternativefor the latter, but discouraged, because these are prone
to be erased acci-dentally.
2.3 Running METAFONT
Processing your document with LATEX will generate one or more
METAFONTles, which you will have to process with METAFONT. On
UNIX11 systems,METAFONT is invoked as
mf '\mode:=hMETAFONT-modei; input hMETAFONT-lei'from the shell.
Here hMETAFONT-lei is to be replaced by the name of theinput le
(which is determined by the argument to the fmffile environment,see
section 2.1) and hMETAFONT-modei is the proper METAFONT-mode for
yourparticular printer. Please consult your local guide or local
wizards about howto run METAFONT on other systems.
11UNIX was a trademark of UNIX Systems Laboratory, but is
rumored to have been donoredto X/Open.
10
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% foo.tex
...
\usepackage{feynmp}
...
\begin{fmffile}{fd}
\begin{fmfchar*}(100,50)
...
\end{fmfchar*}
...
\end{fmffile}
...
% fd.mp -- do not edit
input feynmp
beginchar(1,100*1pt#,50*1pt#,0);
vinit;
...
vfreeze;
vdraw;
endchar;
...
LaTEX labelsfd.t1
LaTEX labelsfd.t2
encapsulatedPostScript
lefd.1
encapsulatedPostScript
lefd.2
device independentoutput lefoo.dvi
printerlpr
latex foo
latex foo
mp fd
dvixx foo
Figure 4: Interdependency of les in a feynMF application using
METAPOST:The arrows show which les are updated in the two LATEX
passes, the META-POST pass and the nal dvi translation step.
Note that hMETAFONT-modei must be specied, otherwise METAFONT
willfail or the resulting font will not be usable.12 You can look
up the correctMETAFONT mode in the le modes.mf that comes with the
METAFONT distri-bution. Among the more common laser printers are
laserjet for HP Laserjetsat 300dpi, ljfour for HP Laserjets at
600dpi, nexthi for NeXT laser printersat 400dpi, etc.A non-trivial
part can be instructing TEX and your favorite dvi-driver how tond
the generated tfm and gf (resp. pk) les. This is highly system
depen-dent and can be trivial (as in the standard UNIX TEX
installations, where nofurther action is required) or almost
impossible without system priviledges (asunder MVS). Please consult
your local guide or wizards on this point. See alsosection 2.9.2
for common problems with dvi drivers.Some recent TEX
implementations (e.g. web2c with kpathsea version 2.6 orlater) are
able to generate tfm les on the y. Using such implementations,
run-ning LATEX twice should suce and METAFONT will be invoked
automagically inthe background. Note however, that the
automagically invoked tools might also
12See section 2.9.1 for the typical error message and for
additional information on printermodes.
11
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install the \fonts" corresponding to the Feynman diagrams in a
system direc-tory, where they don't belong. Adding the following
lines to the maketex.sitescript will prevent this mishap in the
teTEX distribution for UNIX (which isderived from web2c):
if [ -r $KPSE_DOT/$NAME.mf ]; then
MT_PKDESTDIR=$KPSE_DOT
MT_TFMDESTDIR=$KPSE_DOT
MT_NAMEPART=
fi
The automagic tools will also not notice when a diagram has
changed. Theseproblems suggest that it is a generally a good idea
to invoke METAFONT ex-plicitely, instead of relying on the
automagic tools.Running METAPOST is usually trivial, because not
printer specic mode isneeded:
mp hMETAPOST-lei
2.4 The feynmf perl script
UNIX users will be able to take advantage of the feynmf perl
script, that auto-mates the invocation of LATEX and METAPOST. In
particular it tries to guessthe correct METAFONT-mode and
magnication. The latter is often dierentfrom 1 in slide classes.
Here is the man page of feynmf:
NAME
feynmf | Process LaTeX les using FeynMF
SYNOPSIS
feynmf [-hvqncfT] [-t tfm [-t tfm ...]] [-m mode] le [le
...]feynmf [--help] [--version] [--quiet] [--noexec] [--clean]
[--force][--notfm] [--tfm tfm [--tfm tfm ...]] [--mode mode] le [le
...]
DESCRIPTION
The most complicated part of using the FeynMF style appears to
be the properinvocation ofMetafont. The feynmf script provides a
convenient front end andwill automagically invokeMetafont with the
proper mode and magnincation.It will also avoid cluttering system
font directories and oers an option to cleanthem.
OPTIONS
-h, --helpPrint a short help text.
-v, --versionPrint the version of feynmf.
12
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-q, --quietDon't echo the commands being executed.
-n, --noexecDon't execute LaTeX or Metafont.
-c, --cleanOer to delete font les that have accidentally been
placed in a system di-rectory by the MakeTeXTFM and MakeTeXPK
scripts (these scriptsare run by tex (and latex) in the
background). This option has only beentested with recent versions
of UNIX TeX.
-f, --forceDon't ask any questions.
-T, --notfmDon't try to prepare fake .tfm les for the rst
run.
-t, --tfm tfmDon't try guess the names of the .tfm les to fake
for the rst run anduse the given name(s) instead. This option can
be useful if our incompleteparsing of the LaTeX input les
fails.
-m mode, --mode modeSelect the METAFONT mode mode. The default
is guessed or localfontif the guess fails.
leMain LaTeX input les.
le ...Other LaTeX input les that are included by the main
le.
AUTHOR
Thorsten Ohl
BUGS
The preparation of .tfm les is not foolproof yet, because we can
parse TeXles only supercially.This script has only been tested for
recent teTeX distributions of UNIX TeX,though it will probably work
with other versions of UNIX TeX. The author willbe grateful for
portability suggestions, even concerningBorg operating systems,for
the benet of those users that are forced to live with DOS or
Windows.
2.5 Vertex mode
These basic features of feynMF are (or rather \should be")
available throughthe LATEX interface. No knowledge of METAFONT is
necessary.
13
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v1 v2 v3v4
v1
v2
v3
v4
v1
v2v3
v4
v5
v6v7
v1v2 v3 v4
v1
v2
v3
v4
Figure 5: Curved galleries.
v1 v2 v3 v4
v1
v2
v3
v4
v1
v2v3v4
v5v6 v7
v1 v2 v3 v4
v1
v2
v3
v4
Figure 6: Straight galleries.
2.5.1 External vertices
Positioning of external vertices has to done explicitely. The
technical reason is\fmfleft\fmfright
\fmfbottom
\fmftop
\fmfsurround
that they would otherwise collapse with their neighbors, but
practical reasonsalso suggest to give the user full control here.
\fmfleft{hv1 i[,. . . ]} places thevertices in the comma separated
list hv1 i,. . . equidistantly on a smooth pathon the left side of
the diagram. \fmfright{hv1 i[,. . . ]} does the same thing onthe
right. Similarly \fmfbottom and \fmftop, while \fmfsurround{hv1
i[,. . . ]}places its arguments on smooth path surrounding the
diagram.Per default, the galleries on which we place the external
vertices are curved\fmfcurved
\fmfstraight as in gure 5, but straight galleries are also
available. The macros \fmfcurvedand \fmfstraight switch between
these alternatives.The macro \fmfleftn is similar to \fmfleft, but
\fmfleftn{hvi}{hni}\fmfleftn
\fmfrightn
\fmfbottomn
\fmftopn
\fmfsurroundn
places the vertices hv[1]i. . . hv[n]i. Analogously for the
macros \fmfrightn,\fmfbottomn, \fmftopn and \fmfsurroundn.
2.5.2 Arcs and internal vertices
This is the the most frequently used macro in feynMF
applications.\fmf
\fmf{hstylei[,hopti[=hvali],. . . ]}{hv1 i,hv2 i[,. . .
]}connects the vertices v1,v2,. . . with a line of style hstylei,
using a set of optionshopti with (optional) value hvali. If a
vertex is not known yet, it is added tothe diagram. Note that the
actual drawing is not done immediately, becausethe positions can
only be calculated when all vertices are known. The
currentlyavailable styles are collected in table 1. Most names
should be self explanatoryand are not discussed further. The
dashes, dots, phantom and plain stylescan optionally be decorated
with an arrow as shown above. All styles, includingcurly, wiggly
and zigzag, can be doubled. But arrows are not available forthe
latter three, because esthetically pleasing results can not be
expected. Thephantom style is special, because it only enters the
vertices and does not causea line to be drawn. This is extremely
useful for advanced layout features, asexplained below. If you need
a line styles that is not listed in table 1, seesection 2.8.1 for
how to dene your own line styles.
14
-
Name Example Parameters Aliases
curly curly_len gluon
dbl_curly curly_len
dashes dash_len
dashes_arrow dash_len scalar
dbl_dashes dash_len
dbl_dashes_arrow dash_len
dots dot_len
dots_arrow dot_len ghost
dbl_dots dot_len
dbl_dots_arrow dot_len
phantom
phantom_arrow
plain vanilla
plain_arrow fermion, electron, quark
dbl_plain double
dbl_plain_arrow double_arrow, heavy
wiggly wiggly_len boson, photon
dbl_wiggly wiggly_len
zigzag zigzag_width
dbl_zigzag zigzag_len
Table 1: Available line styles
The supported options are collected in table 213 Note that each
of the dotseparated components of the options can be abbreviated.
For example, l.d isequivalent to label.dist. The result of
ambiguous matches is however unde-ned.Note that because the options
are separated by single commata, commata insidearguments to options
(label comes to mind) have to be doubled (similar to
13One particulary useful further option would be smooth,
allowing for several lines joinedsmoothly. Early experimentation
has shown however, that the results are not always whatone expects
and that there is a lot of room for abuse.
15
-
Name Explanation
tension draw a tighter (> 1) or more loose (< 1)arc
left draw on a halfcircle on the leftright draw on a halfcircle
on the rightstraight draw on a straight line (default)label TEX
text for labeling the arclabel.side force placement of the label on
the left
or rightlabel.dist place label at a distance distlabel.pos
relative position of the label (not imple-
mented yet!)tag optional tag for disambiguating arcswidth width
of the linerubout scale factor for crossing out lines
(doesn't work properly for doubled linesyet)
foreground foreground color (METAPOST only!)background
background color for doubled lines
(METAPOST only!)
Table 2: Available line options
quotes in Fortran).14
Arcs that return to their origin are allowed (I will refer to
them as tadpoles),but some options have slightly dierent semantics.
tension is here a inversescale factor for the tadpole, whose
default size is 2/3 of the average distancethe neighboring
vertices. If left or right are specied, they give the direction(in
degrees) of the preferred gap into which the tadpole is placed. By
default,the largest gap is chosen for all tapoles at a given
vertex, which will thereforeoverlap. This is neither a bug nor a
feature, but a limitation.The macro \fmfn is similar to \fmf,
but\fmfn
\fmfn{hstylei[,hopti[=hvali],. . . ]}{hvi}{hni}connects the
vertices hv[1]i. . . hv[n]i.The macro \fmfcyclen{hstylei}{hvi}{hni}
cyclically connects the vertices\fmfcyclen
\fmfrcyclen hv[1]i. . . hv[n]i. \fmfrcyclen operates in reverse
order.Pick up a pen of the specied size. \fmfpen{hweighti} is used
for changing the\fmfpenweight (i.e. thickness) of the lines.
Predened sizes are thin and thick.Declare vertices with
options:\fmfv
\fmfv{hopti[=hvali][,hopti[=hvali],. . . ]}{hv1 i[,. . . ]}This
is used for adding labels to a vertex and for specifying other
decoration.Supported options are collected in table 3. Here the
same abbreviation mecha-nism as above is in eect. The available
shapes are listed in various lling styles
14Note that, as of version 1.03, it is no longer necessary to
escape TEX control sequences inarguments. Old les will continue to
work, because noexpand is temporarily disabled.
16
-
Name Explanation
label TEX text for labeling the vertexlabel.angle force
placement of the label at the given
angle from the vertexlabel.dist place label at a distance
distdecoration.shape shape of decorationdecoration.size size of
decorationdecoration.filled ll, shade or hatch
decorationdecoration.angle rotate decorationforeground foreground
color (METAPOST only!)background background color (METAPOST
only!)
Table 3: Available vertex options
in table 415. The tilings gray10, gray25, gray75 and gray90 are
available in ad-dition to gray50. Customized tilings can be created
with the METAFONT func-tion tile_from_string. It should be noted
however, that tilings are gobblingup memory at high speed and
should be used with discretion. The halftones16
can be accessed by giving any number from 2 to 99, which will
denote the per-centage of saturation (30% and 70% here)17. Again,
commata inside argumentsto options have to be doubled.Draw a blob
of the specied diameter at the vertices. Incidentally,\fmfblob
\fmfblob{hdiameteri}{hv1 i[,. . . ]}is equivalent to
\fmfv{decor.shape=circle,decor.filled=shaded,
decor.size=hdiameteri}{hv1 i[,. . . ]}Draw a dot at the vertices
given as arguments.\fmfdot
\fmfdot{hv1 i[,. . . ]}is equivalent to
\fmfv{decor.shape=circle,decor.filled=full,
decor.size=2thick}{hv1 i[,. . . ]}The macro \fmfvn is similar to
\fmfv, but\fmfvn
\fmfvn{hopti[=hvali][,hopti[=hvali],. . . ]}{hvi}{hni}places the
vertices hv[1]i. . . hv[n]i.The macros \fmfdotn and \fmfblobn are
similar to the \fmfdot and \fmfblob,\fmfdotn
\fmfblobn but \fmfdotn{hvi}{hni} places the vertices hv[1]i. . .
hv[n]i. Analogously for\fmfblobn.
15If the variable feymfwizard is true (e.g. after calling the
\fmfwizard macro), it is alsopossible to specify any METAFONT
expression that evaluates to a path. Naturally, this hasto used
with great care, because strange errors can be triggered by
typos!16METAPOST will give true halftones (if your printer supports
them), while METAFONT
tries to mimic them. The dithering algorithm of the latter will
be improved in the future.17The old numeric arguments in the range
1 : : : 1 continue to work, but are considered
obsolete.
17
-
filled= full empty shaded hatched gray50 30 70
circle
square
triangle
diamond
pentagon ! " #
hexagon $ % & ' ( ) *
triagram + , - . / 0 1
tetragram 2 3 4 5 6 7 8
pentagram 9 : ; < = > ?
hexagram @ A B C D E F
triacross cross pentacross hexacross
G H I J
Table 4: Available vertex shapes and ll styles.
2.5.3 Polygons
Complex vertices with arcs attached at the corners can be
contructed withpolygons, which share some characteristics with arcs
and vertices.The macro\fmfpoly
\fmfpoly{hstylei[,hopti[=hvali],. . . ]}{hv1 i,hv2 i[,. . .
]}places the vertices hv1 i, hv2 i, . . . on the corners of a
regular polygon. Theorientation of the polygon is xed to be
mathematically positive (i.e. counterclockwise). Note that this can
have strange results if the orientation is oppositeto the
orientation of the vertices the corners are connected to. The
availableoptions are collected in table 5. The eects of some
options are depicted intable 6.Note that is is technically
impossible to x the size of a polygon. The size canbe controlled by
specifying a tension for the edges, which acts like the tensionof
normal arcs.The macro \fmfpolyn{hstylei}{hvi}{hni} is similar to
\fmfpoly but connects\fmfpolyn
\fmfrpolyn the vertices hv[1]i. . . hv[n]i. \fmfrpolyn operates
in reverse order.
18
-
Name Explanation
filled ll, shade or hatch interiorphantom don't draw
anythingempty draw outlineshade shade interiorhatched hatch
interiorfull ll interiorpull pull edges in (< 0) or out (>
0)tension tension of the edgessmooth draw smoth cornerslabel TEX
text for labeling the polygonlabel.angle force placement of the
label at the given
angle from the vertexlabel.dist place label at a distance
distforeground foreground color (METAPOST only!)background
background color (METAPOST only!)
Table 5: Available polygon options
2.5.4 Color
If METAPOST is used for rendering the diagrams, vertices and
arcs can becolored. The corresponding options give a warning
message under METAFONTand are otherwise ignored.Two colors are
available for vertices and arcs: foreground and background.Both can
either be specied as a linear combination of the predened
colorswhite, black, red, green and blue or as RBG triples
(hredi,hgreeni,hbluei).Note that as always commata have to be
doubled in option arguments. There-fore both foreground=(1,,0,,1)
and foreground=red+blue are valid optionssetting the foreground
color to magenta. For arcs, the background color is usedonly for
the interior of doubled lines.While the color feature is rarely
used in papers or books, it can be very usefulfor jazzing up your
transparencies. See page 27 for a not very serious example.
2.5.5 Examples
After the main features of the vertex mode have been introduced,
it is time fora couple of illustrative examples that are taken from
The Real World.
As a rst example, consider drawing a straightforward box
diagram, fa-miliar from K- K, D- D, and B- B mixing. The commands
for the labelsare not shown here, they are discussed in section
2.5.6
Let us start the diagram and pick up a thick pen:
\begin{fmfgraph}(40,25)
\fmfpen{thick}
19
-
pull= 0.75 1.0 ? 1.5
default K L M N
smoothO P Q R
default S T U V
smoothW X Y Z
default [ \ ] ^
smooth_ ` a b
Table 6: Some of the available polygon shapes. Note that
pull=1.0 is identicalto pull=? for straight lines, but very dierent
for smooth lines.
The incoming and outcoming vertices are placed on the left and
righthand side, respectively:
\fmfleft{i1,i2}
\fmfright{o1,o2}
Now we tell feynMF how the arcs are connected.
\fmf{fermion}{i1,v1,v3,o1}
\fmf{fermion}{o2,v4,v2,i2}
\fmf{photon}{v1,v2}
\fmf{photon}{v3,v4}
t; c; u
W+ W
t; c; u
b
d
d
b
Finally we tell feynMF to draw dots at the vertices and we're
done.
\fmfdotn{v}{4}
\end{fmfgraph}
20
-
With a little eort the layout of this diagram can actually be
improvedby enlarging the inner box, see page 29 below.
Here is the resonant s-channel contribution to e+e ! 4f . (From
nowon, we do no longer display the
\begin{fmfgraph}(40,25)
\fmfpen{thick}
...
\end{fmfgraph}
environment surrounding all pictures.)
\fmfleftn{i}{2}
\fmfrightn{o}{4}
\fmf{fermion}{i1,v1,i2}
\fmf{photon}{v1,v2}
\fmfblob{.15w}{v2}
\fmf{photon}{v2,v3}
\fmf{fermion}{o1,v3,o2}
\fmf{photon}{v2,v4}
\fmf{fermion}{o4,v4,o3}
e
e+
+
s
c
And the resonant t-channel contribution:
\fmfleftn{i}{2}
\fmfrightn{o}{4}
\fmf{fermion}{i1,v1,v2,i2}
\fmf{photon}{v1,v3}
\fmf{fermion}{o1,v3,o2}
\fmf{photon}{v2,v4}
\fmf{fermion}{o4,v4,o3}
e
e+
+
s
c
Two point loop diagrams pose another set of problems. We must
havea way of specifying that one or more of the lines connecting
the twovertices are not connected by a straight line. The options
left, rightand straight oer the possibility to connect two vertices
by a semicircledetour, either on the left or on the right. Since by
default all lines con-tribute to the tension between two vertices,
the tension option allows usto reduce this tension. The next
examples shows both options in action.The lower fermion line is
given an tension of 1=3 to make is symmetricalwith the upper line
with consists of three parts. The loop photon is usinga detour on
the right and does not contribute any tension.
\fmfleft{i1,i2}
\fmfright{o1}
\fmf{fermion,tension=1/3}{i1,v1}
\fmf{plain}{v1,v2}
\fmf{fermion}{v2,v3}
\fmf{photon,right,tension=0}{v2,v3}
21
-
\fmf{plain}{v3,i2}
\fmf{photon}{v1,o1}
p k
k
p0
p
The optional argument to left and right can be used to deform
thecorresponding contour as in the following example. The default
value ofleft and right is 1.
\fmfleft{i} \fmfright{o}
\fmf{plain}{i,v1} \fmf{plain}{v2,o}
\fmf{dots,left=.5,tension=0.3}{v1,v2,v1}\fmffreeze
\fmf{plain,left}{v1,v2,v1}
\fmf{dashes,left=1.5}{v1,v2,v1}
Polygons are particulary useful for depicting non-perturbative
contribu-tions:
\fmfpen{thick}
\fmfleftn{l}{2}\fmfrightn{r}{2}
\fmfrpolyn{shaded,label=$\Gamma$}{G}{4}
\fmfpolyn{empty,label=$K$}{K}{4}
\fmf{fermion}{l1,G1}\fmf{fermion}{l2,G2}
\fmf{fermion}{K1,r1}\fmf{fermion}{K2,r2}
\fmf{fermion,left=.5,tension=.5}{G3,K3}
\fmf{fermion,right=.5,tension=.5}{G4,K4}
K
To conclude this rst picture show, here's a self energy in
scalar 4-theoryshowing the simplicity of the tadpole feature:
\fmfpen{thick}
\fmfleft{i}
\fmfright{o}
\fmf{plain}{i,v,v,o}
\fmfdot{v}
Scalar 6-theory needs a little manual intervention to force the
second onthe opposite side:
\fmfpen{thick}
\fmfleft{i}
\fmfright{o}
\fmf{plain}{i,v,v,o}
\fmf{plain,left=90}{v,v}
\fmfdot{v}
22
-
2.5.6 Labels
Let us now come back to the examples on page 21 and discuss how
to add thelabels.The macro\fmflabel
\fmflabel{hlabeli}{hvi}is equivalent to
\fmfv{label=hlabeli}{hvi}and adds the label hlabeli to the
vertex hvi. In the current implementation, therecan be only a
single label for each vertex. Thus earlier calls to \fmflabel for
thesame vertex will be overwritten. hlabeli will be placed with the
\put commandof the LATEX picture environment.
18 Note that the fmfgraph* environmentmust be used to use
labels, they will silently disappear in fmfgraph.\fmflabel gives
the user no control on the placement of the the label (use the\fmfv
macro for a more ne-grained control). The label is placed using
thefollowing algorithm:
1. The reference point of the box containing hlabeli is placed
at the distance3thick on the continuation of the straight line
connecting the center ofthe picture with the vertex hvi.
2. The reference point of the box is chosen such that the
contents of the boxis on the outside of the vertex (with respect to
the center of the diagram).It is chosen from the four corners and
the four midpoints of the sides.
Therefore the four external particles in the B- B mixing diagram
on page 21 arelabelled simply by:
\fmflabel{$\bar{b}$}{i1}
\fmflabel{$d$}{i2}
\fmflabel{$\bar{d}$}{o1}
\fmflabel{$b$}{o2}
Here is a more systematical demonstration of the default
placement oflabels:
\fmfsurroundn{v}{8}\fmfdotn{v}{8}
\fmflabel{$v_1$}{v1}
\fmflabel{$v_2$}{v2}
\fmflabel{$v_3$}{v3}
\fmflabel{$v_4$}{v4}
\fmflabel{$v_5$}{v5}
\fmflabel{$v_6$}{v6}
\fmflabel{$v_7$}{v7}
\fmflabel{$v_8$}{v8}
v1
v2
v3v4
v5
v6v7
v8
18Note again that, as of version 1.03, it is no longer necessary
to escape TEX control se-quences in arguments. Old les will
continue to work, because noexpand is temporarily dis-abled.
23
-
And here is a demonstration of the explicit placement of
labels19:
\fmfiv{d.sh=circle,d.f=1,d.si=2thin}{c}
\fmfiv{l=-120,l.a=-120,l.d=.2w}{c}
\fmfiv{l=-60,l.a=-60,l.d=.2w}{c}
\fmfiv{l=0,l.a=0,l.d=.2w}{c}
\fmfiv{l=60,l.a=60,l.d=.2w}{c}
\fmfiv{l=120,l.a=120,l.d=.2w}{c}
\fmfiv{l=180,l.a=180,l.d=.2w}{c}
-120 -60
0
60120
180
There is no equivalent to \fmflabel for arcs. Here options to
the \fmf commandhave to be used. The default placement rules put
the label on the outside at themidpoint of a curved arc. If the arc
is straight, one should use the label.sideoption to push the label
either to the left or to the right. This label.distoption is
treated analogously to same option for vertices.Therefore the four
internal particles in the B- B mixing diagram on page 21
arelabelled simply by adding options to the \fmf commands:
\fmf{fermion,label=$\bar{t},,\bar{c},,\bar{u}$,
label.side=right}{v1,v3}
\fmf{fermion,label=$t,,c,,u$,label.side=right}{v4,v2}
\fmf{photon,label=$W^+$,label.side=left}{v1,v2}
\fmf{photon,label=$W^-$,label.side=right}{v3,v4}
2.5.7 Manipulating the layout
The automatic layout algorithms of feynMF are rather simple,
therefore it issometimes necessary to allow for manual intervention
from time to time.Calculate the positions of the vertices based on
the arcs which are dened up to\fmffreezethis point. Usually this
calculation is performed automatically at the end of thefmfgraph
environment. Calling it explicitely is useful for later adding arcs
thatshould not enter the calculation . The layout is chosen to
minimize the overalllength of all arcs. The length of each arc is
weighted with the tension option,whose default value is 1. See
section 2.5.8 for more information on
\fmffreeze.\fmfforce{hposi}{hv1 i[,. . . ]} forces the position
hposi of the vertices hv1 i. . . ,\fmfforcebypassing and
overwriting the automatic layout. In all arguments that areMETAFONT
pairs (i.e. points), you can use the variable w and h, which are
pre-dened to the width and the height of the whole diagram
respectively. E.g. thecenter is specied as (.5w,.5h) and the lower
right corner as (w,0). The centerand the four corners of the
current subgraph (see the fmfsubgraph environmenton page 29) are
available as c, nw, ne, sw and se (for north-west
etc).\fmfshift{hdisti}{hv1 i[,. . . ]} shifts the position of the
vertices hv1 i. . . by\fmfshifthdisti from the automatic layout.
This command is only useful after a\fmffreeze of the corresponding
vertex.\fmffixed{hdisti}{hv1 i[,. . . ]} xes the distance between
subsequent vertices\fmffixedin the list hv1 i. . . to hdisti. This
command should be used with care, because19Don't be confused by the
\fmfiv command. It is described below (see section 2.7.2) and
takes the same arguments as the \fmfv command. We use it here
for convenience to placemultiple vertices at the same point, i.e.
the center.
24
-
it is possible to overconstrain the layout of the graph and the
error messageswill be obscure for a novice user.\fmffixedx{hdx
i}{hv1 i[,. . . ]} is identical to \fmffixed{(hdx i,whatever)}{hv1
i\fmffixedx
\fmffixedy [,. . . ]} and \fmffixedy{hdyi}{hv1 i[,. . . ]} is
identical to \fmffixed{(whatever,hdyi)}{hv1 i[,. . . ]}. These
commands can be used to x relative positions in one
coordinate,while allowing movement in the other coordinate.
2.5.8 Skeletons
The single most powerful concept for adjusting feynMF's layout
decisions is theuse of skeletons. By issuing a \fmffreeze after
specifying a subgraph (skeleton),we can x the location of the
skeleton as if the other arcs were not there. Wecan then
successively add more subgraphs whose layout will be chosen with
theskeleton remaining xed. Similar eects can be achieved by giving
some arcs avanishing tension.
Consider the following example: suppose we want to draw a ladder
dia-gram contributing to the quark form factor. Simply linking in
the gluonsdoes not produce a satisfactory result:
\fmfleft{i1} \fmfright{o1,o2}
\fmf{photon}{i1,v4}
\fmf{quark}{o1,v1,v2,v3,v4,v5,v6,v7,o2}
\fmf{gluon}{v1,v7}
\fmf{gluon}{v2,v6}
\fmf{gluon}{v3,v5}
What went wrong? Obviously the gluons are bonding the quark
lines toostrongly. The x is simple: just create a skeleton
excluding the gluons
\fmfleft{i1} \fmfright{o1,o2}
\fmf{photon}{i1,v4}
\fmf{quark}{o1,v1,v2,v3,v4,v5,v6,v7,o2}
and add the gluons later:
\fmfleft{i1} \fmfright{o1,o2}
\fmf{photon}{i1,v4}
\fmf{quark}{o1,v1,v2,v3,v4,v5,v6,v7,o2}
\fmffreeze
\fmf{gluon}{v1,v7}
\fmf{gluon}{v2,v6}
\fmf{gluon}{v3,v5}
Alternatively, we can use a vanishing tension, which will
eectively ex-clude the gluons from the layout decisions:
\fmfleft{i1} \fmfright{o1,o2}
\fmf{photon}{i1,v4}
25
-
\fmf{quark}{o1,v1,v2,v3,v4,v5,v6,v7,o2}
\fmf{gluon,tension=0}{v1,v7}
\fmf{gluon,tension=0}{v2,v6}
\fmf{gluon,tension=0}{v3,v5}
Which method is more intuitve is largely a matter of taste and
at thediscretion of the user.
The \crossed" version of this diagram is best drawn using the
ruboutoption:
\fmfleft{i1} \fmfright{o1,o2}
\fmf{photon}{i1,v3}
\fmf{quark}{o1,v1,v2,v3,v4,v5,o2}
\fmffreeze
\fmf{gluon}{v1,v4}
\fmf{gluon,rubout}{v2,v5}
If rubout is selected, it defaults to 2, but it can be changed
to any(reasonable) value > 1. The current implementation should
work foralmost all user-dened line styles. However, it does not
work correctlyfor the predened double line styles yet.
Another instructive example is the following: imagine you want
to drawa typical non-resonant contribution to e+e ! 4f . The
obvious solutiondoesn't look right:
\fmfleft{i1,i2}
\fmfright{o1,o2,o3,o4}
\fmf{fermion}{i1,v1,i2}
\fmf{boson}{v1,v2}
\fmf{fermion}{o1,v2,v3,o4}
\fmf{boson}{v3,v4}
\fmf{fermion}{o3,v4,o2}
Again, we should start with a skeleton
\fmfleft{i1,i2}
\fmfright{o1,o2,o3,o4}
\fmf{fermion}{i1,v1,i2}
\fmf{boson}{v1,v2}
\fmf{fermion}{o1,v2,v3,o4}
and add the second W later:
\fmfleft{i1,i2}
\fmfright{o1,o2,o3,o4}
\fmf{fermion}{i1,v1,i2}
\fmf{boson}{v1,v2}
\fmf{fermion}{o1,v2,v3,o4}
26
-
\fmffreeze
\fmf{boson}{v3,v4}
\fmf{fermion}{o3,v4,o2}
Here's another example that uses stretchable arcs. Diagrams of
this kindare known as rainbow diagrams. If you're using METAPOST
and arewatching this on a color device, you'll see why.
\fmfpen{thick}
\fmfleft{i1,d1}
\fmfright{o1,d2}
\fmfn{plain}{i}{4}
\fmf{plain}{i4,v,o4}
\fmfn{plain}{o}{4}
\fmffreeze
\fmf{gluon,left,fore=red}{i1,o1}
\fmf{gluon,left,fore=green}{i2,o2}
\fmf{gluon,left,fore=blue}{i3,o3}
\fmfdotn{i}{3}
\fmfdotn{o}{3}
\fmfv{d.sh=circle,d.f=empty,d.si=.2w,b=(1,,0,,1),
l=$\Sigma$}{v}
Experience has shown that the method advocated in this section
is more eectivethan fuzzing around with fractional tension
parameters. Using \fmfshift or\fmfforce should be a last resort
only.
2.5.9 Pulling strings
If you add to any arc one or more phantom arcs they will cause a
tighter bondingbetween the vertices involved
\fmf{fermion}{v1,v2}
\fmf{phantom}{v1,v2}
which is equivalent to
\fmf{fermion,tension=2}{v1,v2}
The phantom arc has to be added before any \fmffreeze involving
these ver-tices, of course.
Here is an example from deep inelastic scattering20:
\fmfleft{ip,il}
\fmfright{oq1,oq2,d1,oq3,d2,d3,ol}
\fmf{fermion}{ip,vp,vq,oq3}
20Don't be confused by the \fmfi command. It is described below
(see section 2.7.1) andtakes the same arguments as the \fmfv
command. We use it here for adding to more linesparallel to the
incoming proton line. They do not enter the layout decisions.
27
-
\fmf{fermion}{vp,oq1}
\fmf{fermion}{vp,oq2}
\fmf{photon}{vl,vq}
\fmf{fermion}{il,vl,ol}
\fmfblob{.15w}{vp}
\fmfdot{vq,vl}
\fmffreeze
\fmfi{plain}{vpath (__ip,__vp) shifted (thick*(0,2))}
\fmfi{plain}{vpath (__ip,__vp) shifted (thick*(1,-2))}
As it stands, all vertices come out too far to the right,
because the greaternumber of outgoing lines pulls them over. Adding
\fmf{phantom} makesthe bond between the incoming vertices and the
interactions tighter andproduces a better balanced picture:
\fmfleft{ip,il}
\fmfright{oq1,oq2,d1,oq3,d2,d3,ol}
\fmf{fermion}{ip,vp,vq,oq3}
\fmf{phantom}{ip,vp}
\fmf{fermion}{vp,oq1}
\fmf{fermion}{vp,oq2}
\fmf{photon}{vl,vq}
\fmf{fermion}{il,vl,ol}
\fmf{phantom}{il,vl}
\fmfblob{.15w}{vp}
\fmfdot{vq,vl}
\fmffreeze
\fmfi{plain}{vpath (__ip,__vp) shifted (thick*(0,2))}
\fmfi{plain}{vpath (__ip,__vp) shifted (thick*(1,-2))}
Equivalently, we could add tension to the lines in question and
we willget the same result:
\fmfleft{ip,il}
\fmfright{oq1,oq2,d1,oq3,d2,d3,ol}
\fmf{fermion,tension=2}{ip,vp}
\fmf{fermion}{vp,vq,oq3}
\fmf{fermion}{vp,oq1}
\fmf{fermion}{vp,oq2}
\fmf{photon}{vl,vq}
\fmf{fermion,tension=2}{il,vl}
\fmf{fermion}{vl,ol}
\fmfblob{.15w}{vp}
\fmfdot{vq,vl}
\fmffreeze
\fmfi{plain}{vpath (__ip,__vp) shifted (thick*(0,2))}
\fmfi{plain}{vpath (__ip,__vp) shifted (thick*(1,-2))}
Conversely, specing a tension < 1 will make the corresponding
arcs moreloose.
28
-
Reconsider the box graph on page 20 and reduce the tension on
the innerlines21
\fmfleft{i1,i2}
\fmflabel{$\bar{b}$}{i1}
\fmflabel{$d$}{i2}
\fmfright{o1,o2}
\fmflabel{$\bar{d}$}{o1}
\fmflabel{$b$}{o2}
\fmf{fermion}{i1,v1}
\fmf{fermion,tension=.5,label=$\bar{t},,\bar{c},,\bar{u}$,
l.side=right}{v1,v3}
\fmf{fermion}{v3,o1}
\fmf{fermion}{o2,v4}
\fmf{fermion,tension=.5,label=$t,,c,,u$,l.side=right}{v4,v2}
\fmf{fermion}{v2,i2}
\fmf{photon,tension=.2,label=$W^+$,l.side=left}{v1,v2}
\fmf{photon,tension=.2,label=$W^-$,l.side=right}{v3,v4}
\fmfdotn{v}{4}
t; c; u
W+ W
t; c; u
b
d
d
b
This result is much nicer than the original.
2.6 Miscellaneous commands
2.6.1 Graphs in graphs
The fmfsubgraph environment contains a subgraph, for which the
galleries willfmfsubgraphbe placed inside the rectangle of width
hwidthi and height hheighti, with lowerleft corner at (hx i;
hyi):
\begin{fmfsubgraph}(hx i,hyi)(hwidthi,hheighti)hbodyi
\end{fmfsubgraph}
The center and four corners are available as c, nw, ne, sw and
se (for north-westetc). Because of the restrictions on the overall
size of the diagram in META-FONT, this environment will, mainly be
useful for preparing transparencies withMETAPOST.
Here is a not very serious application of this feature:
\def\subgraphsample#1{%
\fmfleftn{#1i}{2}%
\fmfrightn{#1o}{2}%
\fmf{plain}{#1i1,#1v1}%
\fmf{plain}{#1o1,#1v2}%
\fmf{plain}{#1o2,#1v3}%
\fmf{plain}{#1i2,#1v4}%
\fmfcyclen{plain,tension=0.3}{#1v}{4}}
\begin{fmfgraph}(40,30)
\subgraphsample{a}
21Now that you know, I have also displayed the label options
used.
29
-
\begin{fmfsubgraph}(.3w,.3h)(.4w,.4h)
\subgraphsample{b}
\end{fmfsubgraph}
\begin{fmfsubgraph}(.45w,.45h)(.1w,.1h)
\subgraphsample{c}
\end{fmfsubgraph}
\end{fmfgraph}
More serious applications will use this feature to group
together relateddiagrams and use other METAFONT drawing commands
for graphicalelements that are not available in the LATEX picture
environment.
2.6.2 Reusing diagrams
After saving a pointer with \fmfkeep{hnamei} inside a fmfgraph
or fmfgraph*\fmfkeep\fmfreuse environment, the diagram can be
reused later by \fmfreuse{hnamei}. This
works across fmffile environments.Here's an example that uses
centered \parboxes to place diagrams into equa-tions. The
celebrated cancelation of quadratic divergencies in scalar
selfenergiesin supersymmetric eld theories can be written as:
\begin{eqnarray}
\parbox{20mm}{\begin{fmfgraph}(20,15)\fmfkeep{boson}
\fmfleft{i} \fmfright{o} \fmf{dashes}{i,v,v,o}
\end{fmfgraph}} & \propto & \Lambda^2 \\
\parbox{20mm}{\begin{fmfgraph}(20,15)\fmfkeep{fermion}
\fmfleft{i} \fmfright{o} \fmf{dashes}{i,v1}
\fmf{dashes}{v2,o}
\fmf{fermion,left,tension=.3}{v1,v2,v1}
\end{fmfgraph}} & \propto & \Lambda^2 \\
\parbox{20mm}{\fmfreuse{boson}} \quad + \quad
\parbox{20mm}{\fmfreuse{fermion}} & \propto &
\ln\Lambda^2
\end{eqnarray}
The result is:
/ 2 (1)
/ 2 (2)
+
/ ln2 (3)
2.6.3 Grouping
Make the enclosed \fmfset assignments local to this
environment.fmfgroup
30
-
Parameter Default Semantics
thin 1pt thin arcsthick 1.5thin thicker arcsarrow_len 4mm length
of arrow headarrow_ang 15 opening angle of arrow headcurly_len 3mm
length of one curldash_len 3mm length of one dashdot_len 2mm
distance of two dotswiggly_len 4mm length of one wigglewiggly_slope
60 inclination of wiggleszigzag_len 2mm length of a zig-zag
periodzigzag_width 2thick width of zig-zag linesdecor_size 5mm
default size of vertex decorsdot_size 4thick diameter of dots
Table 7: Available style parameters.
2.6.4 Changing parameters
This command can be used to change the parameters in table 7 as
follows:\fmfset
\fmfset{hparameteri}{hvaluei}Note that these parameters are not
stored in the graph data structure for theindividual vertices and
arcs. Instead the current values at the time of \fmfdraware
used.
2.6.5 Shrinking
Shrink the linewidths and similar parameters in the enclosed
section.fmfshrink
2.6.6 Debugging
Enable and disable tracing of the layout decisions. This is not
necessarily\fmftrace\fmfnotrace printed in an intuitive format, but
can be helpful for debugging.
Enable online displays. \fmfstopdisplay will halt METAFONT
everytime a\fmfdisplay\fmfstopdisplay graph is complete.
2.6.7 Multiple vertices and arcs
The environmentfmffor
\begin{fmffor}{hvari}{hfromi}{hstepi}{htoi}hbodyi
\end{fmffor}
executes hbodyi multiple times, setting hvari to hfromi;
hfromi+hstepi; : : : ; htoi.An application of this above feynMF
feature is shown in gure 7, which isgenerated by calling the TEX
macro
\def\EulerHeisenberg#1{%
31
-
Figure 7: Higher order terms in the Euler-Heisenberg
lagrangian.
\begin{fmfgraph}(40,25)
\fmfpen{thick}
\fmfsurroundn{e}{#1}
\begin{fmffor}{n}{1}{1}{#1}
\fmf{photon}{e[n],i[n]}
\end{fmffor}
\fmfcyclen{fermion,tension=#1/8}{i}{#1}
\end{fmfgraph}}
with the arguments 4, 6, 8, and 10, respectively.Similarly, we
can draw the diagrams from many particle physics in gures 8and
9:
\def\PPRing#1{%
\begin{fmfgraph}(20,20)
\fmfsurroundn{v}{#1}
\fmfdotn{v}{#1}
\fmfcyclen{fermion,right=0.25}{v}{#1}
\fmfcyclen{fermion,left=0.25}{v}{#1}
\end{fmfgraph}}
\def\PHRing#1{%
\begin{fmfgraph}(20,20)
\fmfsurroundn{v}{#1}
\fmfdotn{v}{#1}
\fmfcyclen{fermion,right=0.25}{v}{#1}
\fmfrcyclen{fermion,right=0.25}{v}{#1}
\end{fmfgraph}}
2.7 Immediate mode
In addition to the automatic layout of vertices, feynMF features
an immediatemode, in which feynMF's drawing commands operate
directly on METAFONT's
32
-
Figure 8: Particle-particle ring diagrams
Figure 9: Particle-hole ring diagrams
pairs and paths. You might want to consult The METAFONT Book [4]
or theMETAPOSTmanual [5] for further information on the available
path expressions.
2.7.1 Arcs
Immediate mode's brother of \fmf.\fmfi
\fmfi{hstylei[,hopti[=hvali],. . . ]}{hpi}draws a line of style
hstylei on path hpi. Use the vpath function in hpi (af-ter
\fmffreeze!) to access the METAFONT path connecting two
vertices:vpath[htagi](hfromi,htoi). The optional numeric htagi can
be used togetherwith a matching tag option to \fmf to disambiguate
arcs that connect the samevertices. You have to prepend each name
of a vertex in vpath's arguments withtwo underscores (e.g. v1
becomes __v1). This is necessary for avoiding name-clashes with
some reserved words in METAFONT (sparks in DEK's terminology).
2.7.2 Vertices
Immediate mode's brother of \fmfv.\fmfiv
\fmfiv{hshapei[=hvali][,hopti[=hvali],. . . ]}{hvi}draws a
vertex at position hvi. Note that here hvi is a METAFONT pair and
nota feynMF vertex name. The former's equivalent of the latter can
be accessed(after \fmffreeze!) with the vloc function: vloc(hvertex
i). Again, you haveto prepend the name of the vertex in vloc's
argument with two underscores(e.g. v1 becomes __v1).
2.7.3 Declarations
The argument(s) are declared METAFONT paths.\fmfipathThe
argument(s) are declared METAFONT pairs (coordinates).\fmfipair
33
-
2.7.4 Assignments
Establish equality for the two arguments, i.e.
\fmfiequ{lval}{rval} translates\fmfiequto lval=rval.Assign the
second argument to the rst, i.e. \fmfiset{lval}{rval}
translates\fmfisetto lval:=rval.Specifying equality of two
variables is a very dierent operation from assignmentinMETAFONT.
See TheMETAFONT Book [4] for details onMETAFONT's builtinequation
solver.
2.7.5 Examples
Here is a non-trivial example of immediate mode, which shows
some usefultricks. The non-trivial aspect of the diagram in
question is that it has linesbroken in two, denoting particles
coupling to a condensate.
We start the diagram with a skeleton (the phantom lines are
shown asthin lines for clarity):
\fmfleft{i}
\fmfright{o}
\fmf{dots}{i,v1}
\fmf{dots}{v2,o}
\fmf{phantom,left,tension=0.2,tag=1}{v1,v2}
\fmf{phantom,left,tension=0.2,tag=2}{v2,v1}
\fmfdot{v1,v2}
\fmfposition
Add the fermions to the skeleton
\fmfipath{p[]}
\fmfiset{p1}{vpath1(__v1,__v2)}
\fmfiset{p2}{vpath2(__v2,__v1)}
\fmfi{fermion}{subpath (0,length(p1)/3) of p1}
\fmfi{fermion}{subpath (2length(p1)/3,length(p1)) of p1}
\fmfi{fermion}{subpath (0,length(p2)/3) of p2}
\fmfi{fermion}{subpath (2length(p2)/3,length(p2)) of p2}
Add condensates and a gluon
\def\cond#1#2{%
\fmfiv{d.sh=cross,d.ang=#1,d.siz=5thick}{#2}}
\cond{30}{point length(p1)/3 of p1}
\cond{-30}{point 2length(p1)/3 of p1}
\cond{30}{point length(p2)/3 of p2}
\cond{-30}{point 2length(p2)/3 of p2}
\fmfi{gluon}{point length(p1)/10 of p1
-- point 11length(p1)/12 of p1}
\def\vert#1{%
\fmfiv{d.sh=circle,d.f=1,d.siz=2thick}{#1}}
\vert{point length(p1)/12 of p1}
\vert{point 11length(p1)/12 of p1}
34
-
Figure 10: Circular gluons.
Here's an interesting abuse of feynMF (see the next section for
\fmfcmd):
\begin{fmfgraph*}(40,40)
\fmfipair{o,xm,xp,ym,yp}
\fmfiequ{o}{(.5w,.1h)}
\fmfiequ{xm}{(0,.1h)}
\fmfiequ{xp}{(w,.1h)}
\fmfiequ{ym}{(.5w,0)}
\fmfiequ{yp}{(.5w,h)}
\fmfiv{l=$x$,l.a=-135,l.d=2mm}{xp}
\fmfiv{l=$y=x^2$,l.a=-135,l.d=2mm}{yp}
\fmfpen{thin}
\fmfcmd{draw xm--xp; draw ym--yp;}
\fmfpen{thick}
\fmfiequ{xs}{xpart(xp-o)}
\fmfiequ{ys}{ypart(yp-o)}
\fmfcmd{draw (o + (-xs,ys)) for n = -9 upto 10:
--(o + (xs*(n/10),ys*((n/10)**2)))
endfor;}
\end{fmfgraph*}
x
y = x2
Finally, for the curious, here is how to draw the circular
gluons in gure 10:
\fmfi{gluon}{fullcircle scaled .5w shifted (.5w,.5h)}
\fmfi{gluon}{reverse fullcircle scaled .5w shifted
(.5w,.5h)}
2.8 Raw METAFONT
Some more advanced features of feynMF are more conveniently
accessedthrough raw METAFONT commands. This can either be achieved
by preparinga METAFONT input le or by using \fmfcmd extensively.
The latter apprach isusally more convenient.The \fmfcmdmacro writes
its argument into theMETAFONT input le generated\fmfcmdby feynMF.
While some experience in using METAFONT doesn't hurt here, this
35
-
approach can simplify the production of complex diagrams
considerably. Notethat no semicolon is appended, the user has to
provide it explicitely.
2.8.1 Extending feynMF
A prominent example for using raw METAFONT is provided by the
option to addnew styles for arcs. There is of course always one
more style that must be addedto the default list. But increasing
this list without bounds will eventually slowdown feynMF and
increase its memory requirements. It is therefore better toallow
users to dene their own styles. This is done with the METAFONT
macrostyle_def, which denes a macro that will be called to do the
drawing andregisters this macro with feynMF so that it can be used
in the rst argumentto \fmf.The macro takes one argument of type
path and is responsible for drawing thearc on this path. If
METAPOST's color functionality is to be used, the coloraware
functions cdraw, cfill, cfilldraw, ccutdraw and cdrawdot should
beused instead of draw, etc.
After the following style_def, a new style crossed will be
available:
\fmfcmd{%
vardef cross_bar (expr p, len, ang) =
((-len/2,0)--(len/2,0))
rotated (ang + angle direction length(p)/2 of p)
shifted point length(p)/2 of p
enddef;
style_def crossed expr p =
cdraw p;
ccutdraw cross_bar (p, 5mm, 45);
ccutdraw cross_bar (p, 5mm, -45)
enddef;}
it can be used just like any other style:
\fmfleft{i}
\fmfright{o}
\fmf{plain}{i,v,o}
\fmf{crossed}{v,v}
\fmfdot{v}
And here is an (esthetically questionable!) attempt at wiggly
lines witharrows:
\fmfcmd{%
style_def wiggly_arrow expr p =
cdraw (wiggly p);
shrink (2);
cfill (arrow p);
endshrink;
enddef;}
36
-
Note how the shrink macro (which is the METAFONT equivalent of
thefmfshrink environment) is used to temporarily double the
dimensions ofthe arrowhead which is constructed by the arrow
macro.
In particular theorists beyond the standard model are likely to
need a lotof dierent line styles. The acionados of majorana
neutrinos might ndthe following two useful:
\fmfcmd{%
style_def majorana expr p =
cdraw p;
cfill (harrow (reverse p, .5));
cfill (harrow (p, .5))
enddef;
style_def alt_majorana expr p =
cdraw p;
cfill (tarrow (reverse p, .55));
cfill (tarrow (p, .55))
enddef;}
Note the use of the harrow and tarrow functions which return an
arrow-head on the given fraction of the path, with reference points
at the head(harrow) or tail (tarrow). The arrow function used above
is equivalentto marrow(p,.5), which has the reference point at the
center of the ar-rowhead. Having the three dierent reference point
available is importantfor supporting arcs of substantially diering
lengths.
A problem of the current implementation is that the endpoints of
doublelines don't match smoothly at vertices:
\fmfpen{thick}\fmfleftn{l}{2}\fmfrightn{r}{2}
\fmfpolyn{shaded}{z}{4}
\fmf{dbl_plain_arrow}{l2,z3}
\fmf{dbl_plain_arrow}{l1,z4}
\fmf{dbl_plain_arrow}{z1,r1}
\fmf{dbl_plain_arrow}{z2,r2}
One way around is to add dots of the right size at the vertices
after thearcs have been drawn.
\fmfpen{thick}\fmfleftn{l}{2}\fmfrightn{r}{2}
\fmfpolyn{shaded}{z}{4}
\fmf{dbl_plain_arrow}{l2,z3}
\fmf{dbl_plain_arrow}{l1,z4}
\fmf{dbl_plain_arrow}{z1,r1}
\fmf{dbl_plain_arrow}{z2,r2}
\fmffreeze\fmfdraw
\fmfvn{d.siz=2thick,d.sh=circle}{z}{4}
37
-
Without the \fmffreeze\fmfdraw, the arcs would \know" about
thedots and would be shortened.
A more elegant solution is to dene line styles with dots at the
head,
\fmfcmd{vardef endpoint_dot expr p =
save oldpen; pen oldpen;
oldpen := currentpen;
pickup oldpen scaled 3;
cdrawdot p;
pickup oldpen;
enddef;}
\fmfcmd{style_def hd_double expr p =
draw_double p;
endpoint_dot point infinity of p;
enddef;}
\fmfcmd{style_def hd_dbl_plain_arrow expr p =
draw_hd_double p;
shrink (1.5);
cfill (arrow p);
endshrink;
enddef;}
tail
\fmfcmd{style_def td_double expr p =
draw_double p;
endpoint_dot point 0 of p;
enddef;}
\fmfcmd{style_def td_dbl_plain_arrow expr p =
draw_td_double p;
shrink (1.5);
cfill (arrow p);
endshrink;
enddef;}
or both
\fmfcmd{style_def htd_double expr p =
draw_double p;
endpoint_dot point 0 of p;
endpoint_dot point infinity of p;
enddef;}
\fmfcmd{style_def htd_dbl_plain_arrow expr p =
draw_htd_double p;
shrink (1.5);
cfill (arrow p);
endshrink;
enddef;}
38
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which can be used as follows to give an equivalent result:
\fmfpen{thick}\fmfleftn{l}{2}\fmfrightn{r}{2}
\fmfpolyn{shaded}{z}{4}
\fmf{hd_dbl_plain_arrow}{l2,z3}
\fmf{hd_dbl_plain_arrow}{l1,z4}
\fmf{td_dbl_plain_arrow}{z1,r1}
\fmf{td_dbl_plain_arrow}{z2,r2}
2.9 Common traps, trouble shooting and frequently askedquestions
(FAQs)
2.9.1 ! Value is too large
The following will be one of the most frequent errors:
! Value is too large (4097).
;
beginchar->...rdp:=(EXPR3);w:=hround(charwd*hppp);
h:=...
l.685 ...char(64, 40*2.84526pt#, 25*2.84526pt#, 0)
;
?
It can have one of two causes:
METAFONT was invoked without specifying the mode. This case is
easilyxed by looking up the correct METAFONT mode in the le
modes.mf thatcomes with the METAFONT distribution. This mode must
be specied onthe command line as \mode:=laserjet for HP Laserjets
at 300dpi, as\mode:=ljfour for HP Laserjets at 600dpi, as
\mode:=nexthi for NeXTlaser printers at 400dpi, etc, just to name
three of the more common laserprinters in the physics
community.
The diagrams are too large for the printer at hand. This case is
actuallynot very likely, because even at 1200dpi the diagrams can
be as large as86mm. For the popular laserprinter resolution of
300dpi, even 346mmare possible. Last time I checked, the diagrams
for this manual could begenerated for a Linotype Linotronic 300 at
2540dpi (mode:=linosuper),but failed in the standard proof mode at
2601.72dpi.22 In fact, in thecurrent modes.mf le, the Chelgraph IBX
at 9600dpi and the AlphatypeCRS at 5333 + 1=3dpi are the only
typesetters that can not be used totypeset this manual.23
22It would be trivial to shrink the diagrams by 1% to make them
work in proof mode (acci-dentally, the largest diagram is 40mm
wide, while 4096/2601.72dpi corresponds to 39.99mm).However, I
prefer METAFONT to give an error message if the user forgot to
specify the mode.It is much more obscure when METAFONT works
without errors but the dvi driver fails tond the generated bitmap
le.23If someone wants to use feynMF with one of these high end
typesetters, I would be glad
to try to help them out with kludges.
39
-
2.9.2 Diagrams in the document are never updated
There are two known reasons why diagrams may not be updated the
documentafter the source le has been changed:
Some dvi le previewers (e.g. xdvi(1) under UNIX) do not reread
fontinformation if the tfm or pk les have changed, even though they
rereadthe dvi le if it has changed. Therefore you have to restart
such previewersif you have made changes in diagrams to see these
changes on the screen.
Some dvi drivers (e.g. dvips(1) under UNIX) do not work with the
gfles directly, but convert them with an external program to pk
formatrst. On later occasions, the dvi driver will then use the pk
le which isout of date with respect to the sources and the gf le.
The only knownx is to delete the pk ls before running the dvi
driver.
2.9.3 Disgrams show up in the wrong spot
If you are using feynMF with LATEX's \includeonly feature, you
should watchout for the following situation:
\includeonly{bar1,bar3}
\begin{fmffile}{foograph}
\include{bar1}
\include{bar2}
\include{bar3}
\end{fmffile}
where bar1.tex denes graph #1, bar2.tex graph #2 and bar3.tex
denesgraph #3. If you now proceeded to add graphs to bar1.tex, you
will noticethat a second graph is accepted, but instead of the new
third graph, the oldgraph #3 appears. What happens is that LATEX
stores the value of the counterfor fmfgraphs in each .aux le so
that because bar2.tex is not processed, thiscounter is always reset
to 3 at the beginning of bar3.tex.Even though this situation
appears to be contrived, it actually occured in reallife
applications and the resulting error is very confusing.The only \x"
for this problem would be to use a private counter behind
LATEX'sback. Unfortunately, it appears that this will violate the
principle of minimalsurprise even more. It is therefore usually a
good idea to reprocess the completedocument when the number of
graphs has changed in an \included le. Theother solution is to have
a separate fmfgraph environment for each \includedle.
2.9.4 Spurious labels show up
If spurious labels show up in your diagrams, this is most likely
caused by oldlabel les (e.g. foo.thni) still lying around. Just
delete these les and rerunTEX and METAFONT (or METAPOST
respectively).
40
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2.10 Known bugs
2.10.1 Chaotic manual
This is being worked on. It should probably be rewritten from
scratch, but Idon't have enough time at the moment (this is a spare
time activity).
2.10.2 Delayed error messages
This can't be xed. The problem is that errors can manifest
themselves only along time after the corresponding source line has
been read. Since TEX doesn'tallow to access the current source line
number, there is no way to store thisinformation along with the
other information on the graph. I can only hope tohave enough
sanity checks in place some day that error messages from META-FONT
won't occur.
2.10.3 Multiple tadpoles
Currently, feynMF will not layout multiple tadpoles at a single
vertex auto-matically. This could be xed in principle, but these
xes would cause otherproblems which are more inconvenient than
having to lay out tadpoles manually.
2.10.4 Hard limits
Currently the most severe limitation lies in the size of the
generated pictures.The largest number METAFONT can represent
internally is 4095.99998 and thisis also the largest value any
coordinate measured in pixels can assume. Atthe most popular
laserprinter resolution of 300 dots per inch (dpi), this
corre-sponds to a horizontal and vertical extension of about 346mm,
which is plentyand we're more likely to hit the internal limits on
the complexity of a picture.However, at the proof mode resolution
of 2601.72dpi, this is reduced to slightlyless than 40mm and we're
running the risk of arithmetic overow in internalcalculations much
earlier.There are two potential solutions of dierent scope and
complexity:
Since John Hobby's METAPOST is now available without a
non-disclosureagreement from AT&T, one solution is to replace
METAFONT by META-POST, which doesn't suer from the size
limitations. This comes witha small price paid in reduced
portability of the generated output, but asalready stated above in
the case of axodraw, the ubiquity of PostScriptprinters (and the
free GhostScript interpreter) makes this a minor point.
The more ambitious solutions would be virtual graphs, i.e.
graphs whichare larger than the current limit enforced by numeric
overow at higherresolutions. This could be implemented by
calculating the layout of aminiature graph and afterwards
distributing the full graph among severalMETAFONT characters.
Acknowledgements
I am most grateful to Wolfgang Kilian, who pushed feynMF's
predecessorfeynman.mf to its limits [12]. Discussions with him
triggered a lot of good
41
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ideas. Thanks also to my students and the people on The Net for
suggestions,portability xes and for volunteering as guinea
pigs.
References
[1] Donald E. Knuth, The TEXbook, Addison-Wesley, Reading MA,
1986.
[2] Leslie Lamport, LATEX | A Documentation Preparation System,
Addison-Wesley, Reading MA, 1985.
[3] Michel Goosens, Frank Mittelbach, and Alexander Samarin, The
LATEXCompanion, Addison-Wesley, Reading MA, 1994.
[4] Donald E. Knuth, The METAFONTbook, Addison-Wesley, Reading
MA,1986.
[5] John D. Hobby, A User's Manual for METAPOST, Computer
Science Re-port #162, AT&T Bell Laboratories, April 1992.
[6] Thorsten Ohl, Comp. Phys. Comm. 90 (1995) 340.
[7] Thorsten Ohl, CERN Computer Newsletter 220 (1995) 22; 221
(1995) 46;222 (1996) 24.
[8] Micheal J. S. Levine, Comp. Phys. Comm. 58 (1990) 181.
[9] Jos Vermaseren, Comp. Phys. Comm. 83 (1994) 45. axodraw is
availablefrom CTAN (cf. p. 42), in the graphics directory.
[10] Thomas E. Leathrum, mfpic, available from CTAN (cf. p. 42),
in thegraphics directory.
[11] Tim Stelzer and Bill Long, Comp. Phys. Comm. 81 (1994)
357.
[12] Wolfgang Kilian, Doctoral Thesis, Technical University
Darmstadt, 1994.
[13] Alan Jerey, Lists in TEX's Mouth, TUGboat 199?.
Distribution
feynMF is available by anonymous internet ftp from any of the
ComprehensiveTEX Archive Network (CTAN) hosts
ftp.shsu.edu, ftp.tex.ac.uk, ttp.dante.de
in the directory
macros/latex/contrib/supported/feynmf
It is also available from the host
crunch.ikp.physik.th-darmstadt.de
in the directory
42
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pub/ohl/feynmf
Unsupported snapshots of my work in progress are provided as
pub/ohl/feynmf.versions/feynmf-current.tar.gz
There are two mailing lists
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open for subscription. The former should carry only important
announcements,of new versions in particular. To subscribe, send
mail to the (electronic) mailinglist manager
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and not to the lists itself. The following commands (on a line
in the body ofthe mail, not in the subject) are useful:
subscribe feynmf-announce
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help
Index
Numbers written in italic refer to the page where the
corresponding entry isdescribed; numbers underlined refer to the
code line of the denition; numbersin roman refer to the code lines
where the entry is used.
Symbols-T, {notfm@-T,
--notfm . . . 13-c, {clean@-c, --clean 13-f, {force@-f, --force
13-h, {help@-h, --help 12-m mode, {mode
mode@-mmode, --modemode . . . . . . 13
-n, {noexec@-n,--noexec . . . 13
-q, {quiet@-q,--quiet . . . . 13
-t, {tfm tfm@-t, --tfmtfm . . . . . . . 13
-v, {version@-v,--version . . 12
Aarcs . . . . . . . 14, 16, 33
Bblobs . . . . . . . . . . . . 17
Ccolor . . . . . . . . . . . . 19crossed arcs . . . . . . .
36
Ddening new styles . . 36displays, online . . . . . 31dots . . .
. . . . . . . . . . 17
Eenvironments:
fmffile . . . . . . . 8fmffor . . . . . . . . 31fmfgraph . . . .
. . 9fmfgraph* . . . . . . 9fmfgroup . . . . . . 30fmfshrink . . .
. . . 31fmfsubgraph . . . . 29
extensions . . . . . . . . 36external vertices . . . . 14
Fle ...@le ... . . . . . . 13le@le . . . . . . . . . . 13
\fmf . . . . . . . . . . . . . 14\fmfblob . . . . . . . . .
17\fmfblobn . . . . . . . . 17\fmfbottom . . . . . . .
14\fmfbottomn . . . . . . . 14\fmfcmd . . . . . . . . . .
35\fmfcurved . . . . . . . 14\fmfcyclen . . . . . . . 16\fmfdisplay
. . . . . . . 31\fmfdot . . . . . . . . . . 17\fmfdotn . . . . . .
. . . 17fmffile (environ-
ment) . . . . . . . 8\fmffixed . . . . . . . . 24\fmffixedx . .
. . . . . 25\fmffixedy . . . . . . . 25fmffor (environment)
31\fmfforce . . . . . . . . 24\fmfframe . . . . . . . . 9\fmffreeze
. . . . . . . 24fmfgraph (environ-
ment) . . . . . . . 9fmfgraph* (environ-
ment) . . . . . . . 9
43
-
fmfgroup (environ-ment) . . . . . . 30
\fmfi . . . . . . . . . . . . 33
\fmfiequ . . . . . . . . . 34
\fmfipair . . . . . . . . 33
\fmfipath . . . . . . . . 33
\fmfiset . . . . . . . . . 34
\fmfiv . . . . . . . . . . . 33
\fmfkeep . . . . . . . . . 30
\fmflabel . . . . . . . . 23
\fmfleft . . . . . . . . . 14
\fmfleftn . . . . . . . . 14
\fmfn . . . . . . . . . . . . 16
\fmfnotrace . . . . . . . 31
\fmfpen . . . . . . . . . . 16
\fmfpoly . . . . . . . . . 18
\fmfpolyn . . . . . . . . 18
\fmfrcyclen . . . . . . . 16
\fmfreuse . . . . . . . . 30
\fmfright . . . . . . . . 14
\fmfrightn . . . . . . . 14
\fmfrpolyn . . . . . . . 18
\fmfset . . . . . . . . . . 31
\fmfshift . . . . . . . . 24fmfshrink (environ-
ment) . . . . . . 31\fmfstopdisplay . . . 31\fmfstraight . . . .
. . 14fmfsubgraph (environ-
ment) . . . . . . 29\fmfsurround . . . . . . 14\fmfsurroundn . .
. . . 14\fmftop . . . . . . . . . . 14\fmftopn . . . . . . . . .
14\fmftrace . . . . . . . . 31\fmfv . . . . . . . . . . . .
16\fmfvn . . . . . . . . . . . 17
Ggalleries . . . . . . . . . . 14
Iinternal vertices . 16, 17
Llabels . . . . 14, 16, 23, 24looping . . . . . . . . . . .
31
Oonline displays . . . . . 31OPTIONS . . . . . . . . 12
Pparameters . . . . . . . . 31polygons . . . . . . . . . .
18
Rrunning METAFONT . 10running METAPOST . 12
Sstyles, dening new . . 36subgraphs . . . . . . . . . 29
Ttadpoles . . . . . . . . . . 22tracing . . . . . . . . . . .
31
Vvertices . . . . . . . . . . 33vertices, external . . . .
14vertices, internal . 16, 17
44